Subgroups — C₇×#60399 #13237615

Order 1792.

5128 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3484	C₂	1	3	yes	maximal, complemented
3	C₇×#3027	C₂	1	4	yes	maximal, complemented
4	C₇×#3026	C₂	1	8	yes	maximal, complemented
5	C₇×#3025	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×B(4,𝔽₂)	C₂	1	8	yes	maximal, complemented
7	C₇×#2883	C₂	1	3	yes	maximal, complemented
8	C₇×#585	—	2	12	no	—
9	C₇×#585	C₂²	1	4	yes	complemented
10	C₂×C₇×H(5,𝔽₂)	—	2	12	no	—
11	C₂×C₇×H(5,𝔽₂)	C₂²	1	3	yes	—
12	C₂×C₇×H(5,𝔽₂)	C₂²	1	8	yes	complemented
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₇×#546	—	2	12	no	—
15	C₇×D₄²	—	2	12	no	—
16	C₇×#535	C₂²	1	6	yes	complemented
17	C₇×#534	C₂²	1	12	yes	complemented
18	C₇×#525	C₂²	1	6	yes	complemented
19	C₂×C₇×#120	C₂²	1	12	yes	complemented
20	C₇×#518	C₂²	1	3	yes	complemented
21	C₇×#458	C₂²	1	16	yes	complemented
22	C₇×B(4,𝔽₂)	C₂²	1	16	yes	complemented
23	C₇×B(4,𝔽₂)	C₂²	1	32	yes	complemented
24	C₇×#410	C₂²	1	12	yes	complemented
25	C₂×C₇×#99	C₂²	1	24	yes	complemented
26	#60399	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂⁵×C₇	C₂³	1	2	yes	complemented
28	C₇×2₋¹⁺⁴	—	2	16	no	—
29	C₇×2₋¹⁺⁴	—	2	12	no	—
30	C₇×H(5,𝔽₂)	—	2	48	no	—
31	C₇×H(5,𝔽₂)	—	2	24	no	—
32	C₇×H(5,𝔽₂)	—	2	12	no	—
33	C₇×H(5,𝔽₂)	—	2	48	no	—
34	C₇×H(5,𝔽₂)	C₂³	1	16	yes	—
35	C₂×C₇×#41	—	2	48	no	—
36	C₂×C₇×#41	—	2	24	no	—
37	C₂×C₇×#41	—	2	24	no	—
38	C₂×C₇×#41	D₄	1	12	yes	complemented
39	C₂×C₇×#41	C₂³	1	6	yes	—
40	C₂²×C₇×D₄	—	2	16	no	—
41	C₂²×C₇×D₄	—	2	24	no	—
42	C₂²×C₇×D₄	—	2	12	no	—
43	C₂²×C₇×D₄	—	2	12	no	—
44	C₂²×C₇×D₄	D₄	1	12	yes	complemented
45	C₂²×C₇×D₄	C₂³	1	12	yes	—
46	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
47	C₂²×C₇×D₄	C₂³	1	2	yes	complemented
48	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
49	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic, complemented
50	C₇×#127	—	2	6	no	—
51	C₇×#124	—	2	6	no	—
52	C₇×#123	—	2	12	no	—
53	C₇×#123	C₂³	1	12	yes	complemented
54	C₇×C₂²⋊Q₈	—	2	6	no	—
55	C₇×#121	—	2	6	no	—
56	C₇×#121	—	2	24	no	—
57	C₇×#121	—	2	12	no	—
58	C₇×#120	—	2	12	no	—
59	C₇×#120	—	2	24	no	—
60	C₇×#120	C₂³	1	12	yes	complemented
61	C₇×#120	C₂³	1	24	yes	complemented
62	C₄×C₇×D₄	—	2	12	no	—
63	C₄×C₇×D₄	—	2	12	no	—
64	C₇×#117	C₂³	1	6	yes	complemented
65	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
66	C₂×C₇×C₂²⋊C₄	C₂³	1	12	yes	complemented
67	C₇×#99	C₂³	1	48	yes	complemented
68	H(7,𝔽₂)	C₂×C₇	1	1	yes	characteristic, complemented
69	#3484	C₂×C₇	1	3	yes	complemented
70	#3027	C₂×C₇	1	4	yes	complemented
71	#3026	C₂×C₇	1	8	yes	complemented
72	#3025	C₂×C₇	1	4	yes	complemented
73	C₂×B(4,𝔽₂)	C₂×C₇	1	8	yes	complemented
74	#2883	C₂×C₇	1	3	yes	complemented
75	C₂⁴×C₇	—	2	8	no	—
76	C₂⁴×C₇	—	2	12	no	—
77	C₂⁴×C₇	—	8	4	no	—
78	C₂⁴×C₇	C₂×D₄	1	12	yes	complemented
79	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
80	C₂⁴×C₇	C₂⁴	1	2	yes	—
81	C₂⁴×C₇	C₂⁴	1	2	yes	—
82	C₇×#41	—	2	96	no	—
83	C₇×#41	—	2	48	no	—
84	C₇×#41	—	2	16	no	—
85	C₇×#41	—	2	48	no	—
86	C₇×#41	—	2	48	no	—
87	C₇×#41	—	2	24	no	—
88	C₂×C₇×Q₈	—	2	24	no	—
89	C₂×C₇×Q₈	—	2	8	no	—
90	C₂×C₇×Q₈	C₂×D₄	1	6	yes	complemented
91	C₂×C₇×D₄	—	2	96	no	—
92	C₂×C₇×D₄	—	2	24	no	—
93	C₂×C₇×D₄	—	2	24	no	—
94	C₂×C₇×D₄	—	2	48	no	—
95	C₂×C₇×D₄	—	2	48	no	—
96	C₂×C₇×D₄	—	2	48	no	—
97	C₂×C₇×D₄	—	2	12	no	—
98	C₂×C₇×D₄	—	2	12	no	—
99	C₂×C₇×D₄	—	2	24	no	—
100	C₂×C₇×D₄	—	2	6	no	—
101	C₂×C₇×D₄	—	4	16	no	—
102	C₂×C₇×D₄	—	8	24	no	—
103	C₂×C₇×D₄	C₂×D₄	1	12	yes	—
104	C₂×C₇×D₄	C₂×D₄	1	24	yes	complemented
105	C₂×C₇×D₄	C₂×D₄	1	6	yes	complemented
106	C₂×C₇×D₄	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₇	—	2	24	no	—
108	C₂²×C₄×C₇	—	2	16	no	—
109	C₂²×C₄×C₇	—	2	12	no	—
110	C₂²×C₄×C₇	—	2	6	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	12	yes	complemented
112	C₂²×C₄×C₇	C₂×D₄	1	12	yes	complemented
113	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
115	C₇×C₄⋊C₄	—	2	6	no	—
116	C₇×C₄⋊C₄	—	2	12	no	—
117	C₇×C₂²⋊C₄	—	2	12	no	—
118	C₇×C₂²⋊C₄	—	2	12	no	—
119	C₇×C₂²⋊C₄	—	2	12	no	—
120	C₇×C₂²⋊C₄	—	2	24	no	—
121	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
122	C₄²×C₇	—	2	6	no	—
123	#585	—	2	12	no	—
124	#585	C₂²×C₇	1	4	yes	complemented
125	C₂×H(5,𝔽₂)	—	2	12	no	—
126	C₂×H(5,𝔽₂)	C₂²×C₇	1	3	yes	—
127	C₂×H(5,𝔽₂)	C₂²×C₇	1	8	yes	complemented
128	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
129	#546	—	2	12	no	—
130	D₄²	—	2	12	no	—
131	#535	C₂²×C₇	1	6	yes	complemented
132	#534	C₂²×C₇	1	12	yes	complemented
133	#525	C₂²×C₇	1	6	yes	complemented
134	C₂×#120	C₂²×C₇	1	12	yes	complemented
135	#518	C₂²×C₇	1	3	yes	complemented
136	#458	C₂²×C₇	1	16	yes	complemented
137	B(4,𝔽₂)	C₂²×C₇	1	16	yes	complemented
138	B(4,𝔽₂)	C₂²×C₇	1	32	yes	complemented
139	#410	C₂²×C₇	1	12	yes	complemented
140	C₂×#99	C₂²×C₇	1	24	yes	complemented
141	C₂³×C₇	—	2	16	no	—
142	C₂³×C₇	—	2	3	no	—
143	C₂³×C₇	—	2	24	no	—
144	C₂³×C₇	—	2	6	no	—
145	C₂³×C₇	—	4	2	no	—
146	C₂³×C₇	—	4	24	no	—
147	C₂³×C₇	—	4	8	no	—
148	C₂³×C₇	—	8	2	no	—
149	C₂³×C₇	—	8	2	no	—
150	C₂³×C₇	—	8	12	no	—
151	C₂³×C₇	—	8	12	no	—
152	C₂³×C₇	—	16	8	no	—
153	C₂³×C₇	C₂²×D₄	1	12	yes	—
154	C₂³×C₇	C₂²×D₄	1	12	yes	—
155	C₂³×C₇	C₂⁵	1	1	yes	characteristic
156	C₇×Q₈	—	2	16	no	—
157	C₇×Q₈	—	2	12	no	—
158	C₇×D₄	—	2	48	no	—
159	C₇×D₄	—	2	48	no	—
160	C₇×D₄	—	2	24	no	—
161	C₇×D₄	—	2	12	no	—
162	C₇×D₄	—	4	24	no	—
163	C₇×D₄	—	4	8	no	—
164	C₇×D₄	—	4	4	no	—
165	C₇×D₄	—	8	24	no	—
166	C₇×D₄	#120	1	16	yes	—
167	C₂×C₄×C₇	—	2	48	no	—
168	C₂×C₄×C₇	—	2	24	no	—
169	C₂×C₄×C₇	—	2	24	no	—
170	C₂×C₄×C₇	—	2	12	no	—
171	C₂×C₄×C₇	—	2	3	no	—
172	C₂×C₄×C₇	—	4	4	no	—
173	C₂×C₄×C₇	—	8	12	no	—
174	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
175	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
176	C₂⁵	C₂³×C₇	1	2	yes	complemented
177	2₋¹⁺⁴	—	2	16	no	—
178	2₋¹⁺⁴	—	2	12	no	—
179	H(5,𝔽₂)	—	2	48	no	—
180	H(5,𝔽₂)	—	2	24	no	—
181	H(5,𝔽₂)	—	2	12	no	—
182	H(5,𝔽₂)	—	2	48	no	—
183	H(5,𝔽₂)	C₂³×C₇	1	16	yes	—
184	C₂×#41	—	2	48	no	—
185	C₂×#41	—	2	24	no	—
186	C₂×#41	—	2	24	no	—
187	C₂×#41	C₇×D₄	1	12	yes	complemented
188	C₂×#41	C₂³×C₇	1	6	yes	—
189	C₂²×D₄	—	2	16	no	—
190	C₂²×D₄	—	2	24	no	—
191	C₂²×D₄	—	2	12	no	—
192	C₂²×D₄	—	2	12	no	—
193	C₂²×D₄	C₇×D₄	1	12	yes	complemented
194	C₂²×D₄	C₂³×C₇	1	12	yes	—
195	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
196	C₂²×D₄	C₂³×C₇	1	2	yes	complemented
197	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic, complemented
198	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic, complemented
199	#127	—	2	6	no	—
200	#124	—	2	6	no	—
201	#123	—	2	12	no	—
202	#123	C₂³×C₇	1	12	yes	complemented
203	C₂²⋊Q₈	—	2	6	no	—
204	#121	—	2	6	no	—
205	#121	—	2	24	no	—
206	#121	—	2	12	no	—
207	#120	—	2	12	no	—
208	#120	—	2	24	no	—
209	#120	C₂³×C₇	1	12	yes	complemented
210	#120	C₂³×C₇	1	24	yes	complemented
211	C₄×D₄	—	2	12	no	—
212	C₄×D₄	—	2	12	no	—
213	#117	C₂³×C₇	1	6	yes	complemented
214	C₂×C₂²⋊C₄	—	2	12	no	—
215	C₂×C₂²⋊C₄	C₂³×C₇	1	12	yes	complemented
216	#99	C₂³×C₇	1	48	yes	complemented
217	C₂²×C₇	—	2	6	no	—
218	C₂²×C₇	—	2	12	no	—
219	C₂²×C₇	—	4	12	no	—
220	C₂²×C₇	—	4	1	no	—
221	C₂²×C₇	—	4	12	no	—
222	C₂²×C₇	—	4	3	no	—
223	C₂²×C₇	—	4	12	no	—
224	C₂²×C₇	—	4	1	no	—
225	C₂²×C₇	—	4	2	no	—
226	C₂²×C₇	—	8	24	no	—
227	C₂²×C₇	—	8	16	no	—
228	C₂²×C₇	—	8	16	no	—
229	C₂²×C₇	C₂×#120	1	8	yes	—
230	C₂²×C₇	C₂³×D₄	1	3	yes	—
231	C₄×C₇	—	2	12	no	—
232	C₄×C₇	—	4	12	no	—
233	C₄×C₇	—	4	1	no	—
234	C₄×C₇	C₂×#120	1	4	yes	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	12	no	—
237	C₂⁴	—	8	4	no	—
238	C₂⁴	C₂×C₇×D₄	1	12	yes	complemented
239	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
240	C₂⁴	C₂⁴×C₇	1	2	yes	—
241	C₂⁴	C₂⁴×C₇	1	2	yes	—
242	#41	—	2	96	no	—
243	#41	—	2	48	no	—
244	#41	—	2	16	no	—
245	#41	—	2	48	no	—
246	#41	—	2	48	no	—
247	#41	—	2	24	no	—
248	C₂×Q₈	—	2	24	no	—
249	C₂×Q₈	—	2	8	no	—
250	C₂×Q₈	C₂×C₇×D₄	1	6	yes	complemented
251	C₂×D₄	—	2	96	no	—
252	C₂×D₄	—	2	24	no	—
253	C₂×D₄	—	2	24	no	—
254	C₂×D₄	—	2	48	no	—
255	C₂×D₄	—	2	48	no	—
256	C₂×D₄	—	2	48	no	—
257	C₂×D₄	—	2	12	no	—
258	C₂×D₄	—	2	12	no	—
259	C₂×D₄	—	2	24	no	—
260	C₂×D₄	—	2	6	no	—
261	C₂×D₄	—	4	16	no	—
262	C₂×D₄	—	8	24	no	—
263	C₂×D₄	C₂×C₇×D₄	1	12	yes	—
264	C₂×D₄	C₂×C₇×D₄	1	24	yes	complemented
265	C₂×D₄	C₂×C₇×D₄	1	6	yes	complemented
266	C₂×D₄	C₂⁴×C₇	1	12	yes	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	—	2	16	no	—
269	C₂²×C₄	—	2	12	no	—
270	C₂²×C₄	—	2	6	no	—
271	C₂²×C₄	C₂×C₇×D₄	1	12	yes	complemented
272	C₂²×C₄	C₂×C₇×D₄	1	12	yes	complemented
273	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
275	C₄⋊C₄	—	2	6	no	—
276	C₄⋊C₄	—	2	12	no	—
277	C₂²⋊C₄	—	2	12	no	—
278	C₂²⋊C₄	—	2	12	no	—
279	C₂²⋊C₄	—	2	12	no	—
280	C₂²⋊C₄	—	2	24	no	—
281	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
282	C₄²	—	2	6	no	—
283	C₂×C₇	—	2	3	no	—
284	C₂×C₇	—	2	8	no	—
285	C₂×C₇	—	4	2	no	—
286	C₂×C₇	—	4	12	no	—
287	C₂×C₇	—	8	2	no	—
288	C₂×C₇	C₂²×#120	1	1	yes	characteristic
289	C₂³	—	2	16	no	—
290	C₂³	—	2	3	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	6	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	4	24	no	—
295	C₂³	—	4	8	no	—
296	C₂³	—	8	2	no	—
297	C₂³	—	8	2	no	—
298	C₂³	—	8	12	no	—
299	C₂³	—	8	12	no	—
300	C₂³	—	16	8	no	—
301	C₂³	C₂²×C₇×D₄	1	12	yes	—
302	C₂³	C₂²×C₇×D₄	1	12	yes	—
303	C₂³	C₂⁵×C₇	1	1	yes	characteristic
304	Q₈	—	2	16	no	—
305	Q₈	—	2	12	no	—
306	D₄	—	2	48	no	—
307	D₄	—	2	24	no	—
308	D₄	—	2	48	no	—
309	D₄	—	2	12	no	—
310	D₄	—	4	24	no	—
311	D₄	—	4	8	no	—
312	D₄	—	4	4	no	—
313	D₄	—	8	24	no	—
314	D₄	C₇×#120	1	16	yes	—
315	C₂×C₄	—	2	48	no	—
316	C₂×C₄	—	2	24	no	—
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	3	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	8	12	no	—
322	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
323	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
324	C₇	#60399	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²	—	2	6	no	—
326	C₂²	—	2	12	no	—
327	C₂²	—	4	12	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	12	no	—
330	C₂²	—	4	3	no	—
331	C₂²	—	4	12	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	8	24	no	—
335	C₂²	—	8	16	no	—
336	C₂²	—	8	16	no	—
337	C₂²	C₂×C₇×#120	1	8	yes	—
338	C₂²	C₂³×C₇×D₄	1	3	yes	—
339	C₄	—	2	12	no	—
340	C₄	—	4	12	no	—
341	C₄	—	4	1	no	—
342	C₄	C₂×C₇×#120	1	4	yes	—
343	C₂	—	2	3	no	—
344	C₂	—	2	8	no	—
345	C₂	—	4	2	no	—
346	C₂	—	4	12	no	—
347	C₂	—	8	2	no	—
348	C₂	C₂²×C₇×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	C₂²×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂²×C₇×D₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×H(7,𝔽₂)	C₂	semidirect
2. C₇×#3484	C₂	semidirect
3. C₇×#3027	C₂	semidirect
4. C₇×#3026	C₂	semidirect
5. C₇×#3025	C₂	semidirect
6. C₂×C₇×B(4,𝔽₂)	C₂	semidirect
7. C₇×#2883	C₂	semidirect
9. C₇×#585	C₂²	semidirect
12. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
13. C₂³×C₇×D₄	C₂²	semidirect
16. C₇×#535	C₂²	semidirect
17. C₇×#534	C₂²	semidirect
18. C₇×#525	C₂²	semidirect
19. C₂×C₇×#120	C₂²	semidirect
20. C₇×#518	C₂²	semidirect
21. C₇×#458	C₂²	semidirect
22. C₇×B(4,𝔽₂)	C₂²	semidirect
23. C₇×B(4,𝔽₂)	C₂²	semidirect
24. C₇×#410	C₂²	semidirect
25. C₂×C₇×#99	C₂²	semidirect
26. #60399	C₇	direct (N × H)
27. C₂⁵×C₇	C₂³	semidirect
38. C₂×C₇×#41	D₄	semidirect
44. C₂²×C₇×D₄	D₄	semidirect
47. C₂²×C₇×D₄	C₂³	semidirect
48. C₂²×C₇×D₄	C₂³	semidirect
49. C₂³×C₄×C₇	C₂³	semidirect
53. C₇×#123	C₂³	semidirect
60. C₇×#120	C₂³	semidirect
61. C₇×#120	C₂³	semidirect
64. C₇×#117	C₂³	semidirect
66. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
67. C₇×#99	C₂³	semidirect
68. H(7,𝔽₂)	C₂×C₇	semidirect
69. #3484	C₂×C₇	semidirect
70. #3027	C₂×C₇	semidirect
71. #3026	C₂×C₇	semidirect
72. #3025	C₂×C₇	semidirect
73. C₂×B(4,𝔽₂)	C₂×C₇	semidirect
74. #2883	C₂×C₇	semidirect
78. C₂⁴×C₇	C₂×D₄	semidirect
90. C₂×C₇×Q₈	C₂×D₄	semidirect
104. C₂×C₇×D₄	C₂×D₄	semidirect
105. C₂×C₇×D₄	C₂×D₄	semidirect
111. C₂²×C₄×C₇	C₂×D₄	semidirect
112. C₂²×C₄×C₇	C₂×D₄	semidirect
124. #585	C₂²×C₇	semidirect
127. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
128. C₂³×D₄	C₂²×C₇	semidirect
131. #535	C₂²×C₇	semidirect
132. #534	C₂²×C₇	semidirect
133. #525	C₂²×C₇	semidirect
134. C₂×#120	C₂²×C₇	semidirect
135. #518	C₂²×C₇	semidirect
136. #458	C₂²×C₇	semidirect
137. B(4,𝔽₂)	C₂²×C₇	semidirect
138. B(4,𝔽₂)	C₂²×C₇	semidirect
139. #410	C₂²×C₇	semidirect
140. C₂×#99	C₂²×C₇	semidirect
176. C₂⁵	C₂³×C₇	semidirect
187. C₂×#41	C₇×D₄	semidirect
193. C₂²×D₄	C₇×D₄	semidirect
196. C₂²×D₄	C₂³×C₇	semidirect
197. C₂²×D₄	C₂³×C₇	semidirect
198. C₂³×C₄	C₂³×C₇	semidirect
202. #123	C₂³×C₇	semidirect
209. #120	C₂³×C₇	semidirect
210. #120	C₂³×C₇	semidirect
213. #117	C₂³×C₇	semidirect
215. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
216. #99	C₂³×C₇	semidirect
238. C₂⁴	C₂×C₇×D₄	semidirect
250. C₂×Q₈	C₂×C₇×D₄	semidirect
264. C₂×D₄	C₂×C₇×D₄	semidirect
265. C₂×D₄	C₂×C₇×D₄	semidirect
271. C₂²×C₄	C₂×C₇×D₄	semidirect
272. C₂²×C₄	C₂×C₇×D₄	semidirect
324. C₇	#60399	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×H(7,𝔽₂)	2
C₇×#3484	2
C₇×#3027	2
C₇×#3026	2
C₇×#3025	2
C₂×C₇×B(4,𝔽₂)	2
C₇×#2883	2
#60399	7

Subgroups — C7×#60399 #13237615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60399 #13237615